Logarithmic function Stumped!!
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Logarithmic function Stumped!!

[From: ] [author: ] [Date: 11-07-08] [Hit: ]
!log(A) = 4.log(A[0]) = -1.M = 4.5 - (-1.M = 4.......
Does anyone know how to figure this out?? The magnitude M of an earthquake can be calculated by the formula M=log[base 10] (A/(A[base0]) where A is the maximum amplitude of a seismic wave and A[base0] is a standard amplitude used for comparison. Find the magnitude,M, of a quake when log[base10]A=4.5 and log[base10]A[base0]=-1.8 round answer to one decimal place!!

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M = log(A / A[0])
M = log(A) - log(A[0])

log(A) = 4.5
log(A[0]) = -1.8

M = 4.5 - (-1.8)
M = 4.5 + 1.8
M = 6.3

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First, when you say log [A/ A sub 0], it is understood that it is log base 10, so that should save you some trouble next time. Furthermore, the formula is not A{base 0} but A{sub 0}. That part might be confusing you.
Property you need to know:
log(m/n) = log(m) - log(n)
Thus log[A / Asub 0] = logA - logAsub0
logA = 4.5
logAsub 0 = -1.8
logA - logAsub0 = 4.5 - (-1.8) = 4.5 + 1.8 = 6.3
6.3 is the magnitude

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M=log(10)[A/A0]=>
M=log(10)A-log(10)A0=>
M=4.5-(-1.8)=>
M=6.3
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